Simulation of metal sheet roll forming
Roll forming is an industrial manufacturing process where an initially flat metal sheet sustains incremental plastic bending as it passes through a series of roll stands. The final cross section shape is obtained by irreversible plastic bending deformation; membrane strains remain small.
Description of the implemented model
Presently available commercial simulation tools make use of full 3D continuum models in the Lagrangian kinematic description; an applicable but computationally very expensive approach.
We strive for a more efficient solution and develop a finite element model that features:
- the geometrically nonlinear Kirchhoff–Love theory of shells, which reduces the total number of degrees of freedom in comparison to full 3D continuum models
- the mixed Eulerian–Lagrangian kinematic description, which is more suitable for the axially moving metal sheet than the traditional Lagrangian perspective.
Figure 2: 3D visualization of the finite element simulation model
A particular challenge lies in the account of the elastic-plastic material behavior. The usual way to treat plasticity within a structural theory is the through-the-thickness integration that superimposes the structural kinematics on a continuum element to perform a thickness integration of stress resultants by virtue of the elastic-plastic constitutive law treated in integration points. However, since this approach is computationally demanding, we pursue the development of a novel stress resultant plasticity model. In this model the yield criterion and its evolution by means of a hardening law that properly resolves the continued plastification of the through-the-thickness element need to be formulated in terms of the shell stress resultants and further state variables.
We validate the proposed model against reference computations with commercial software and also against a continuum plasticity model. This comparison demonstrates the capabilities of the proposed scheme to accurately simulate the forming process at significantly reduced computational cost.
Kocbay, Emin, Jakob Scheidl, Fabian Riegler, Martin Leonhartsberger, Matthias Lamprecht, and Yury Vetyukov. "Mixed Eulerian–Lagrangian modeling of sheet metal roll forming, opens an external URL in a new window." Thin-Walled Structures 186 (2023): 110662.
Kocbay, Emin, and Yury Vetyukov. "Stress resultant plasticity for plate bending in the context of roll forming of sheet metal, opens an external URL in a new window" International Journal for Numerical Methods in Engineering 122, no. 18 (2021): 5144-5168.
Vetyukov, Yu, P. G. Gruber, M. Krommer, J. Gerstmayr, I. Gafur, and G36086201378 Winter. "Mixed Eulerian–Lagrangian description in materials processing: deformation of a metal sheet in a rolling mill, opens an external URL in a new window" International Journal for Numerical Methods in Engineering 109, no. 10 (2017): 1371-1390.